Expression of type Conditional

from the theory of proveit.logic.booleans.conjunction

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprRange, Function, P, Pk, Variable, i, j, k
from proveit.logic import And, Forall, Implies, InSet
from proveit.numbers import Integer, Interval

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Forall(instance_param_or_params = [P], instance_expr = Implies(And(ExprRange(sub_expr1, Function(P, [sub_expr1]), i, j)), Forall(instance_param_or_params = [k], instance_expr = Pk, domain = Interval(i, j)))), And(InSet(i, Integer), InSet(j, Integer)))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{\forall_{P}~\left(\left(P\left(i\right) \land  P\left(i + 1\right) \land  \ldots \land  P\left(j\right)\right) \Rightarrow \left[\forall_{k \in \{i~\ldotp \ldotp~j\}}~P\left(k\right)\right]\right) \textrm{ if } i \in \mathbb{Z} ,  j \in \mathbb{Z}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 19 operand: 5
2	Operation	operator: 17 operands: 4
3	ExprTuple	5
4	ExprTuple	6, 7
5	Lambda	parameter: 29 body: 9
6	Operation	operator: 31 operands: 10
7	Operation	operator: 31 operands: 11
8	ExprTuple	29
9	Operation	operator: 12 operands: 13
10	ExprTuple	38, 14
11	ExprTuple	39, 14
12	Literal
13	ExprTuple	15, 16
14	Literal
15	Operation	operator: 17 operands: 18
16	Operation	operator: 19 operand: 22
17	Literal
18	ExprTuple	21
19	Literal
20	ExprTuple	22
21	ExprRange	lambda_map: 23 start_index: 38 end_index: 39
22	Lambda	parameter: 34 body: 24
23	Lambda	parameter: 33 body: 25
24	Conditional	value: 26 condition: 27
25	Operation	operator: 29 operand: 33
26	Operation	operator: 29 operand: 34
27	Operation	operator: 31 operands: 32
28	ExprTuple	33
29	Variable
30	ExprTuple	34
31	Literal
32	ExprTuple	34, 35
33	Variable
34	Variable
35	Operation	operator: 36 operands: 37
36	Literal
37	ExprTuple	38, 39
38	Variable
39	Variable